In this research, we have considered the convective heat transfer analysis on peristaltic flow of Rabinowitsch fluid through an elliptical cross section duct. The Pseudoplastic and Dilatant characteristics of non-Newtonian fluid flow are analyzed in detail. The Rabinowitsch fluid model shows Pseudoplastic fluid nature for $$\sigma > 0$$ σ > 0 and Dilatant fluid behaviour for $$\sigma < 0.$$ σ < 0 . The governing equations are transformed to dimensionless form after substituting pertinent parameters and by applying the long wavelength approximation. The non-dimensional momentum and energy equations are solved analytically to obtain the exact velocity and exact temperature solutions of the flow. A novel polynomial of order six having ten constants is introduced first time in this study to solve the energy equation exactly for Rabinowitsch fluid flow through an elliptic domain. The analytically acquired solutions are studied graphically for the effective analysis of the flow. The flow is found to diminish quickly in the surrounding conduit boundary for Dilatant fluid as compared to the Pseudoplastic fluid. The temperature depicted the opposite nature for Pseudoplastic and Dilatant fluids. The flow is examined to plot the streamlines for both Pseudoplastic and Dilatant fluids by rising the flow rate.
In this research, the electro-osmotic effects are highlighted for a blood-based hybrid nanofluid flow across an artery infected with multiple stenosis. The artery has permeable walls together with slip boundary effects. The slip and permeable boundary conditions model the more realistic blood flow problems. The governing equations of the problem are converted into non-dimensional form by introducing adequate dimensionless variables and acquired the exact solutions. The detailed study of heat transfer is given by Joule heating and viscous dissipation effects. The disorder of fluid flow is investigated by the mathematical study of entropy generation. Analytically attained solutions are examined graphically for both symmetric and non-symmetric shapes of stenosis. Streamlines are analyzed for varying values of flow rate Q and electro-osmotic parameter m. The flow velocity has smallest values on the axis of channel and gets higher value near the boundary walls. The temperature profile delineates opposite behavior to the velocity, and it is parabolic in nature. The velocity reduces towards the non-uniform stenosis except for electroosmotic parameter m. The temperature has larger magnitude in the case of anti-symmetric stenosis. Moreover, the stability of velocity solution is also analyzed.
The occurrence and growth of stenosis effectively interrupt the blood flow in the artery, which may result in vascular disease. It makes the study of blood flow in the artery narrowed with crucial stenosis. This work studies the non-Newtonian nature of blood flow in a diseased artery with an elliptic cross-section. The artery is harmed due to several stenosis, which diminishes its lumen. The Phan-Thein–Tanner fluid is considered to analyze the non-Newtonian characteristics of blood. The Phan-Thein–Tanner fluid model is much suitable for blood flow analysis because of its viscoelastic and shear thinning properties. The governing equations are processed to dimensionless form by employing dimensionless variables and assumptions for a mild stenosis case. The solutions of the nondimensional equations are acquired analytically. The visual examination of the exact solutions is discussed in detail. The fluid velocity is strongly affected by stenosis height, and a more significant disorder is generated in the constricted region with the growing size of stenosis. The flow velocity is found as a decreasing function of the Weissenberg number. The velocity profile is parabolic and axisymmetric as well. The most significant and least influential physical constraints are identified by completing the local sensitivity analysis.
This work consists of the analytical study of the peristaltic flow of heated non-Newtonian fluid flow through an elliptical duct. The flow characteristics of Pseudoplastic and Dilatant fluids are analyzed in a vertically held elliptic duct by considering the Rabinowitsch fluid model. The mathematical model is processed to a dimensionless analysis by employing adequate nondimensional variables and extended wavelength approximation. The resulting PDEs are solved analytically in the elliptic domain using the explicit boundary condition form. A simpler second-degree polynomial is presented to get the solution of temperature. These analytical solutions are examined in detail by graphical analysis. It is found that the flow velocity of Pseudoplastic fluid is more prominent than Dilatant fluid in the vicinity of the centerline. The earlier and later fluids have a maximum axial speed at the channel’s mean and close to the peristaltic boundary. The greater buoyancy force (Grashof number) enhances the Pseudoplastic fluid’s velocity but diminishes the flow velocity of Dilatant fluid. Moreover, it is noticed that the aspect ratio has less impact, and the Grashof number has an effective influence on pressure rise. The streamlines of Rabinowitsch fluid break into vortices near the deformed wall. The vortices are comparatively less in the count for Dilatant fluid than Pseudoplastic fluid for quick flow and a more significant Grashof number.
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